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Finding max/min of 3d graphs with chain rule

  1. Mar 31, 2008 #1
    http://math.berkeley.edu/~theojf/Midterm2Practice.pdf [Broken]

    can someone please help me on problem number 2 of the link above?
    apologies for the bad handwriting. my professor is just horrible with that.

    i've done max and min with multivariables before and ive done chain rule , but i've never combined the two. also, in that problem, the only critical point seems to be a saddle point, so i'm not sure what the "lowest" point is referring to
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Mar 31, 2008 #2


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    You don't need to use the chain rule- in fact you don't need to worry about multi-variables at all. Replace x and y in z(x,y) with their expressions in terms of t and differentiate with respect to t. There are two critical points. One is a minimum and the other a maximum.
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